STA 2201 s 2011 Assignment Three:

Your written answers and printouts are due at the beginning of class Friday on Feb. 18. You may be asked to present your solution to the class before handing it in.

  1. The usual large sample likelihood ratio test was first described by Wilks (1938) in the Annals of Mathematical Statistics (Vol. 9, pp 60-62). This paper is available online through the U of T library using your UTORID if you want to take a look. Just search the catalogue for Annals of Mathematical Statistics. The null hypothesis considered by Wilks is that a subset of the parameters equal fixed values, while the rest of the parameters can be anything. In all the sources I have been able to find (for example, in The Advanced Theory of Statistics by Stuart and Ord), this is how H0 is stated.
    1. We would at least like to be able to test linear null hypotheses of the form H0: Lθ=h. Show that this is possible, starting with Wilks' version.
    2. Even better would be more general null hypotheses. I cannot find anything! Can you? If so please give the source. We need something with a proof, not just a general discussion.
  2. The file logreg.data has data for a logistic regression with three independent variables. Test

    H0: β1 = 2 β0, β1 + β2 = β3

    in two different ways, in each case producing a chisquare statistic, degrees of freedom and p-value. Circle the answers on your printout(s).